Compactons: Solitons with finite wavelength

Feb 1, 1993
3 pages
Published in:
  • Phys.Rev.Lett. 70 (1993) 564-567

Citations per year

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Abstract: (APS)
The understand the role of nonlinear dispersion in pattern formation, we introduce and study Korteweg–de Vries–like equations wtih nonlinear dispersion: ut+(um)x+(un)xxx=0, m,n>1. The solitary wave solutions of these equations have remarkable properties: They collide elastically, but unlike the Korteweg–de Vries (m=2, n=1) solitons, they have compact support. When two ‘‘compactons’’ collide, the interaction site is marked by the birth of low-amplitude compacton-anticompacton pairs. These equations seem to have only a finite number of local conservation laws. Nevertheless, the behavior and the stability of these compactons is very similar to that observed in completely integrable systems.
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